10. LOOKBACK TIME

The lookback time tL to an object is the difference between
the age t0 of the Universe now (at observation) and
the age te
of the Universe at the time the photons were emitted (according to the
object). It is used to predict properties of high-redshift objects
with evolutionary models, such as passive stellar evolution for
galaxies. Recall that E (z) is the time derivative of the logarithm
of the scale factor a (t); the scale factor is proportional to
(1 + z), so the product (1 + z) E (z) is
proportional to the
derivative of z with respect to the lookback time, or

(29)

(Peebles 1993,
pp. 313-315;
Kolb & Turner 1990,
pp. 52-56, give
some analytic solutions to this equation, but they are concerned with
the age t (z), so they integrate from z to ). The lookback
time is plotted in Figure 6.

Figure 6. The dimensionless lookback time
tL / tH and age t / tH.
The three curves are for
the three world models, (M, ) =
(1, 0), solid; (0.05, 0), dotted; and (0.2, 0.8), dashed.